how do you calculate the frequency of a 2.500 m long pendulum in Quito, Ecuador, where g= 9.780 m/s^2
To calculate the frequency of a pendulum, we can use the formula:
Frequency = 1 / Period
where the period of a pendulum is the time it takes for one complete oscillation. The period can be calculated using:
Period = 2π * √(Length / g)
Now, we can plug in the given values. The length of the pendulum is 2.500 m, and the acceleration due to gravity (g) in Quito, Ecuador is 9.780 m/s^2.
Period = 2π * √(2.500 / 9.780)
To calculate the square root of 2.500 divided by 9.780, first divide these values: 2.500 / 9.780 ≈ 0.255.
Then, take the square root of this result: √(0.255) ≈ 0.505.
Now, let's substitute this value back into the period formula:
Period = 2π * 0.505
Multiply π (pi) by 2 and then multiply the result by 0.505:
Period ≈ 3.17 seconds (rounded to two decimal places)
Finally, to find the frequency, we can use the formula Frequency = 1 / Period:
Frequency = 1 / 3.17 ≈ 0.32 Hz (rounded to two decimal places)
Therefore, the frequency of a 2.500 m long pendulum in Quito, Ecuador, with a gravitational acceleration of 9.780 m/s^2, is approximately 0.32 Hz.